// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ROTATION2D_H
#define EIGEN_ROTATION2D_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  * \class Rotation2D
  *
  * \brief Represents a rotation/orientation in a 2 dimensional space.
  *
  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
  *
  * This class is equivalent to a single scalar representing a counter clock wise rotation
  * as a single angle in radian. It provides some additional features such as the automatic
  * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
  * interface to Quaternion in order to facilitate the writing of generic algorithms
  * dealing with rotations.
  *
  * \sa class Quaternion, class Transform
  */

namespace internal {

    template <typename _Scalar> struct traits<Rotation2D<_Scalar>>
    {
        typedef _Scalar Scalar;
    };
}  // end namespace internal

template <typename _Scalar> class Rotation2D : public RotationBase<Rotation2D<_Scalar>, 2>
{
    typedef RotationBase<Rotation2D<_Scalar>, 2> Base;

public:
    using Base::operator*;

    enum
    {
        Dim = 2
    };
    /** the scalar type of the coefficients */
    typedef _Scalar Scalar;
    typedef Matrix<Scalar, 2, 1> Vector2;
    typedef Matrix<Scalar, 2, 2> Matrix2;

protected:
    Scalar m_angle;

public:
    /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
    EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}

    /** Default constructor wihtout initialization. The represented rotation is undefined. */
    EIGEN_DEVICE_FUNC Rotation2D() {}

    /** Construct a 2D rotation from a 2x2 rotation matrix \a mat.
    *
    * \sa fromRotationMatrix()
    */
    template <typename Derived> EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m) { fromRotationMatrix(m.derived()); }

    /** \returns the rotation angle */
    EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }

    /** \returns a read-write reference to the rotation angle */
    EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }

    /** \returns the rotation angle in [0,2pi] */
    EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const
    {
        Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
        return tmp < Scalar(0) ? tmp + Scalar(2 * EIGEN_PI) : tmp;
    }

    /** \returns the rotation angle in [-pi,pi] */
    EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const
    {
        Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
        if (tmp > Scalar(EIGEN_PI))
            tmp -= Scalar(2 * EIGEN_PI);
        else if (tmp < -Scalar(EIGEN_PI))
            tmp += Scalar(2 * EIGEN_PI);
        return tmp;
    }

    /** \returns the inverse rotation */
    EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }

    /** Concatenates two rotations */
    EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const { return Rotation2D(m_angle + other.m_angle); }

    /** Concatenates two rotations */
    EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other)
    {
        m_angle += other.m_angle;
        return *this;
    }

    /** Applies the rotation to a 2D vector */
    EIGEN_DEVICE_FUNC Vector2 operator*(const Vector2& vec) const { return toRotationMatrix() * vec; }

    template <typename Derived> EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
    EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;

    /** Set \c *this from a 2x2 rotation matrix \a mat.
    * In other words, this function extract the rotation angle from the rotation matrix.
    *
    * This method is an alias for fromRotationMatrix()
    *
    * \sa fromRotationMatrix()
    */
    template <typename Derived> EIGEN_DEVICE_FUNC Rotation2D& operator=(const MatrixBase<Derived>& m) { return fromRotationMatrix(m.derived()); }

    /** \returns the spherical interpolation between \c *this and \a other using
    * parameter \a t. It is in fact equivalent to a linear interpolation.
    */
    EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
    {
        Scalar dist = Rotation2D(other.m_angle - m_angle).smallestAngle();
        return Rotation2D(m_angle + dist * t);
    }

    /** \returns \c *this with scalar type casted to \a NewScalarType
    *
    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
    * then this function smartly returns a const reference to \c *this.
    */
    template <typename NewScalarType> EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType>>::type cast() const
    {
        return typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType>>::type(*this);
    }

    /** Copy constructor with scalar type conversion */
    template <typename OtherScalarType> EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
    {
        m_angle = Scalar(other.angle());
    }

    EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }

    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
    * determined by \a prec.
    *
    * \sa MatrixBase::isApprox() */
    EIGEN_DEVICE_FUNC bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
    {
        return internal::isApprox(m_angle, other.m_angle, prec);
    }
};

/** \ingroup Geometry_Module
  * single precision 2D rotation type */
typedef Rotation2D<float> Rotation2Df;
/** \ingroup Geometry_Module
  * double precision 2D rotation type */
typedef Rotation2D<double> Rotation2Dd;

/** Set \c *this from a 2x2 rotation matrix \a mat.
  * In other words, this function extract the rotation angle
  * from the rotation matrix.
  */
template <typename Scalar>
template <typename Derived>
EIGEN_DEVICE_FUNC Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
{
    EIGEN_USING_STD(atan2)
    EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime == 2 && Derived::ColsAtCompileTime == 2, YOU_MADE_A_PROGRAMMING_MISTAKE)
    m_angle = atan2(mat.coeff(1, 0), mat.coeff(0, 0));
    return *this;
}

/** Constructs and \returns an equivalent 2x2 rotation matrix.
  */
template <typename Scalar> typename Rotation2D<Scalar>::Matrix2 EIGEN_DEVICE_FUNC Rotation2D<Scalar>::toRotationMatrix(void) const
{
    EIGEN_USING_STD(sin)
    EIGEN_USING_STD(cos)
    Scalar sinA = sin(m_angle);
    Scalar cosA = cos(m_angle);
    return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
}

}  // end namespace Eigen

#endif  // EIGEN_ROTATION2D_H
